I have a circle of unknown diameter. I do, however, know the length of a chord and the distance between the centre of the circle and the centre of the chord.
Please see picture here where I have added some sample values: I want to determine the value of d
UPDATE: Diagram illustrating maxmilgram's solution below here
The solution in summary is: because we know lines $MN$ and $NP$ an well as angle $∠PNM$ we can solve using simple trig!
Lets call the center point of the circle $M$, the two endpoints of the chord (="diamenter line") $P$ and $Q$ and the midpoint of the chord $N$.
Now observe that the distance between $M$ and $P$ is $r=d/2$, the distance between $N$ and $M$ is $h$ and the distance between $N$ and $P$ is $x/2$. Furthermore the angle $\angle PMN$ is $90°$. Can you take it from there?